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Frontiers in Optics

Hyper-entangled photons

Julio T. Barreiro, Nathan K. Langford, Nicholas A. Peters, Paul G. Kwiat

Published Jan 1, 2005• 0 citations
Publisher

Abstract

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyper-entangled). Using pairs of photons produced in spontaneous parametric downconversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode and time-energy. We also produce and characterize maximally hyper-entangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2x2x3x3 system (36-dimensional Hilbert space), which we believe is the first reported entangled system of this size to be so characterized.

DOI
10.1364/ls.2005.lmb3

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We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyper-entangled). Using pairs of photons produced in spontaneous parametric downconversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode and time-energy. We also produce and characterize maximally hyper-entangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2x2x3x3 system (36-dimensional Hilbert space), which we believe is the first reported entangled system of this size to be so characterized.
We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and time energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2 x 2 x 3 x 3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.
We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an SSS parameter of $S=2.653\ifmmode\pm\else\textpm\fi{}0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.
We experimentally investigate the properties of hyperentangled states displaying simultaneous entanglement in multiple degrees of freedom and find that Bell tests beyond the standard Clauser-Horne-Shimony-Holt inequality can reveal a higher-dimensional nature in a device-independent way. Specifically, we show that hyperentangled states possess more than just simultaneous entanglement in separate degrees of freedom but also entanglement in a higher-dimensional Hilbert space. We also verify the steerability of hyperentangled quantum states by steering different photonic degrees of freedom.
Summary form only given. Entanglement, a fundamental resource of quantum technologies, is a unique quantum mechanical attribute. In various systems it can be achieved in various individual degrees of freedom, however some of those systems are able to create entanglement in multiple degrees of freedom simultaneously: hyper-entanglement [1]. Here, we report on demonstration of polarization [2] and time-bin [3] hyper-entangled photons emitted from a single quantum dot. By applying two-photon resonant and coherent excitation on a quantum dot system with marginal fine structure splitting we yield fidelities to the maximally entangled state of 0.80(3) and 0.87(4) in polarization and time-bin, respectively. Quantum enhanced communication schemes rely on Bell-state measurements, which find their simplest realization in the interference of two photons at a beam splitter. However, this method is efficiency limited [4] and a complete Bell state analysis of a photon pair entangled in one degree of freedom using only linear optics is impossible. This limitation can be overcome if the photon pair is entangled in more than one degree of freedom, a hyper-entangled state. Using such states in such schemes does not only reduce the resource overhead [5] it also offers the possibility to increase the success rate significantly [6].
Two photon states entangled in polarization and momentum, hyper-entangled, have been generated by using linear optics and a single Type I nonlinear crystal. These states have been completely characterized and their nonlocal behaviour have been verified by independent Bell's inequalities tests performed in the two degrees of freedom of entanglement and by an "all versus nothing" test of local realism. The manipulation of these states may represent a useful control in quantum state engineering and Bell state measurements and, more in general, in Quantum Information applications.